1. Field of the Invention
The present disclosure relates to optical microlithography, and more particularly to mask design.
2. Description of the Related Art
Optical Proximity Correction (OPC) involves making systematic modifications to mask geometries in lithography to increase the achievable resolution and pattern transfer fidelity for IC manufacturing. This is accomplished by compensating mask geometry for known effects which will occur during imaging or subsequent processing.
The essential part of a proximity correction apparatus is a simulation engine that provides an accurate simulation of the on-wafer shape, given an input shape on the mask. Conventional simulation engines use the Sum of Coherent Systems (SOCS) method, in which on-wafer light intensity for partially coherent illumination is decomposed into an incoherent sum of intensities from a nominally infinite number of coherent systems. For each particular “coherent system”, a design geometry with a corresponding kernel is computed, and the magnitude of the image intensity from the design geometry is an addend in the sum of coherent sources. To be practical, the SOCS method uses only a finite number of terms, N, where N is chosen to provide a required degree of accuracy. The number N represents the number of kernels.
Increasing N improves SOCS accuracy, but also increases computation time and run time memory requirements. Since integrated circuit masks may contain hundreds of millions of shapes which must be corrected, computation time is at a premium, so it is important to make an efficient choice of kernels. It can be shown that the most efficient set of coherent kernels is obtained by making a Mercer expansion of the bilinear imaging operator (for example, the Hopkins imaging model that is shown as equation 1 below), so that the kernels are the weighted eigenfunctions of the imaging operator. Other choices (for example, forming a separate coherent kernel from each small element of the illumination source) are known to be less efficient. This is shown, for example, in Y. C. Pati and T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11, no. 9 (1994): p. 2438.
In the current state-of-the-art proximity correction systems, the number of kernels N is chosen manually before starting the simulation process based on ad hoc recommendations of simulation tool providers. A small number of test cases is performed to determine if the recommended N provides the required accuracy. Another factor to consider in the determination of the proper N is the possible occurrence of an X/Y asymmetry artifact. X/Y asymmetry artifacts may cause the OPC process to apply different corrections to each instance of the same shape, depending on the shape orientation. This in turn may lead to different behavior of cells that are meant to be identical, which is highly undesirable.
Conventionally, to avoid asymmetry, N is increased until asymmetry is eliminated or negligible. However, such a manual approach is not reliable and can greatly increase turn-around time if the asymmetry is overlooked at the beginning of the process. The problem is especially acute in situations that deal with an optical model having variable parameters or with a multiplicity of different optical models. Thus, there is a need for a process in which N is chosen automatically to optimize accuracy and prevent X/Y asymmetry artifacts.